This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Here's a solution from Matthew (Nimbin Central School,
Australia). He found that 252 lenses would be needed to make all
the glasses. He explained how he did it by first working out all
the combinations of glasses that made up the 9 orders:
"I wrote down in a grid that was eight wide and nine down, 3 or
4 and we had to be careful not to get the same number of threes or
fours as another group of eight. And at the end we found out that
there were 36 fours and 36 threes, and when we added all of the
numbers together it equalled 252".
Is there another way to do the maths in this problem?